Heart of Algebra
If a/b = 2, what is the value of 4b/a?
What is 2?
In the graph of y = 2x^2 + 10x +12, the
graph crosses the y-axis at the point (0,k) what is the
value of k?
A) 2 B) 6 C) 10 D) 12
What is 12?
If y = kx, where k is a constant, and y = 24 when x = 6, what is the value of y when x = 5 ?
What is 20?
what is the sum (7 + 3i) + (−8 + 9i) ?
What is -1+12i?
If (x− 1)/3=k and k = 3, what is the value of x ?
What is 10?
A line in the xy-plane passes through the origin and has a slope of 1/7. Which of the following points lies on the line?
A (0, 7) B (1, 7) C (7, 7) D (14, 2)
What is D?
x2-1 / x-1 = -2
What are all the values of x that satisfy the equation above?
a. -3 b. 0 c. 1 d. -3 and -1
what is -3
A helicopter, initially hovering 40 feet above the ground, begins to gain altitude at a rate of 21 feet per second. Which of the following functions represents the helicopter’s altitude above the ground y, in feet, t seconds after the helicopter begins to gain altitude?
A. y = 40+21 B. y = 40+21t
C. y = 40−21t D. y = 40t +21
What is y=40 + 21t
A right circular cone has a volume of 24π cubic inches. If the height of the cone is 2 inches, what is the radius, in inches, of the base of the cone?
A. 2 times sq. root of 3 B. 6
C. 12 D. 36
What is 6?
On Saturday afternoon, Armand sent m text messages each hour for 5 hours, and Tyrone sent p text messages each hour for 4 hours. Which of the following represents the total number of messages sent by Armand and Tyrone on Saturday afternoon?
What is 5m+4p?
The posted weight limit for a covered wooden bridge in Pennsylvania is 6000 pounds. A delivery truck that is carrying x identical boxes each weighing 14 pounds will pass over the bridge. If the combined weight of the empty delivery truck and its driver is 4500 pounds, what is the maximum possible value for x that will keep the combined weight of the truck, driver, and boxes below the bridge’s posted weight limit?
What is 107?
h = − 4.9t^2 + 25t The equation above expresses the approximate height h, in meters, of a ball t seconds after it is launched vertically upward from the ground with an initial velocity of 25 meters per second. After approximately how many seconds will the ball hit the ground?
What is 5.1?
Katarina is a botanist studying the production of pears by two types of pear trees. She noticed that Type A trees produced 20 percent more pears than Type B trees did. Based on Katarina’s observation, if the Type A trees produced 144 pears, how many pears did the Type B trees produce?
What is 120?
Which of the following is an equation of a circle in the xy-plane with center (0, 4) and a radius with endpoint (4/3, 5)?
What is x^2+(y-4)^2=25/9
Kathy is a repair technician for a phone company. Each week, she receives a batch of phones that need repairs. The number of phones that she has left to fix at the end of each day can be estimated with the equation P = 108 − 23d, where P is the number of phones left and d is the number of days she has worked that week. What is the meaning of the value 108 in this equation?
What is Kathy will start each week with 108 phones to fix?
Wyatt can husk at least 12 dozen ears of corn per hour and at most 18 dozen ears of corn per hour. Based on this information, what is a possible amount of time, in hours, that it could take Wyatt to husk 72 dozen ears of corn?
What is any number between 4-6 inclusive?
y = - (x - 3)2 + a
In the equation above, a is a constant.
The graph of the equation in the xy-plane is a parabola.
Which of the following is true about the parabola?
A) Its minimum occurs at (−3, a)
B) Its minimum occurs at a (3, a)
C) Its maximum occurs at (−3, a)
D) Its maximum occurs at (3, a)
What is "its maximum occurs at (3,a)"?
A local television station sells time slots for programs in 30-minute intervals. If the station operates 24 hours per day, every day of the week, what is the total number of 30-minute time slots the station can sell for Tuesday and Wednesday?
What is 96?
A dairy farmer uses a storage silo that is in the shape of the right circular cylinder with height 8. If the volume of the silo is 72π cubic yards, what is the diameter of the base of the cylinder, in yards?
What is 6?
h = 3a + 28.6 A pediatrician uses the model above to estimate the height h of a boy, in inches, in terms of the boy’s age a, in years, between the ages of 2 and 5. Based on the model, what is the estimated increase, in inches, of a boy’s height each year?
What is 3?
y<-x+a, y>x+b In the xy-plane, if (0, 0) is a solution to the system of inequalities above, which of the following relationships between a and b must be true?
What is a>b
2/3 (9x-6) - 4 = 9x - 6
Based on the equation above, what is the value
of 3x −2 ?
A. −4 B. −4 / 5 C. −2 / 3 D. 4
What is -4?
In the xy-plane, the graph of the function
f(x)= x^2 +5x+4 has two x-intercepts.
What is the distance between the x-intercepts?
what is 3?
700, 1200, 1600, 2000, X
If the mean of the five numbers above is 1600,
what is the value of x ?
What is 2500?
The peregrine falcon can reach speeds of up to 200 miles per hour while diving to catch prey, making it the fastest animal on the planet when in a dive. What is a peregrine falcon’s maximum speed while diving to catch prey, in feet per second?
(Round your answer to the nearest whole number. 1mile=5280feet)
What is 293?